A new type of large-scale signature change in emergent modified gravity

Abstract

Emergent modified gravity presents a new class of gravitational theories in which the structure of space-time with Riemannian geometry of a certain signature is not presupposed. Relying on crucial features of a canonical formulation, the geometry of space-time is instead derived from the underlying dynamical equations for phase-space degrees of freedom together with a crucial covariance condition. Here, a large class of spherically symmetric models is solved analytically for Schwarzschild-type black-hole configurations with generic modification functions, using a variety of slicings that explicitly demonstrates general covariance. For some choices of the modification functions, a new type of signature change is found and evaluated. In contrast to previous versions discussed for instance in models of loop quantum gravity, signature change happens on timelike hypersurfaces in the exterior region of a black hole where it is not covered by a horizon. A large region between the horizon and the signature-change hypersurface may nevertheless be nearly classical, such that the presence of a signature-change boundary around Lorentzian space-time, or a Euclidean wall around the universe, is consistent with observations provided signature change happens sufficiently far from the black hole.